Rewrite as a simplified fraction. ${0.\overline{52} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 52.5252...\\ 1x &= 0.5252...\end{align*}}$ Subtracting the two equations, we have: ${99x = 52}$ ${x = \dfrac{52}{99}} $